Depending on which historian you believe, the British monarchy may trace its roots back as far as the 9th century. It's an extraordinary legacy. It also means that when the monarchy first got started, Indigenous Australians had already forged at least a 38,000-year bond with the Australian continent.

This weekend's eighth anniversary of the apology to the Stolen Generations puts a national spotlight on the ongoing disadvantage of Aboriginal and Torres Strait Islander Australians. It is right that we do this, just as this week has seen the government bring down the eighth Closing the Gap Report. In 2016, persistent racial gaps in health, employment and education are a national disgrace.

We should apologise for the wrongs that were committed, and recommit to closing the gaps that exist. But we should also be proud of our Indigenous people. How cool is it, I tell my kids, that we share this continent with a people who have the longest continuing link to the land in the world? Indigenous Australians have been here for at least 40,000 years, and perhaps as long as 125,000 years.

To celebrate the traditional owners, I believe it's time that we replaced the monarch's face on our coins with faces of some of our most significant Indigenous people. When we toss a coin and call 'heads', I believe it should be an Indigenous Australian face we're hoping to see.

It's true that our $2 coin carries the face of Aboriginal man Gwoya Jungarai. But the other five coins in regular circulation currently bear Her Majesty's visage.

For example, our coins could acknowledge Bungaree (1775-1830), an adventurer who helped Flinders circumnavigate Australia; Truganini (1812-1876) who suffered at the hands of white settlers to Tasmania; or soldier Reg Saunders (1920-1990). In the political realm, we might recognise Eddie Mabo (1936-1992), whose case led the High Court to overturn terra nullius; Vincent Lingiari (1908-1988), who led the Wave Hill walk off, and told Gough Whitlam 'we are all mates now'; or Neville Bonner (1922-1999), the first Indigenous person to serve in federal parliament.

And then there are the creators. Wouldn't it be inspiring to have coins that celebrate musician Mandawuy Yunupingu (1956-2013), poet and writer Oodgeroo Noonuccal (1920-1993), or artist Albert Namatjira (1902-1959)? On the sporting field, we might acknowledge Doug Nicholls (1906-1988), an AFL player and social activist who became South Australian Governor.

Naturally, I've only listed Indigenous people who have passed away. But I'm sure others could suggest more names. If I've omitted your favourite Indigenous Australian, that only serves to reinforce the point. Our first people have made such proud achievements that mentioning just a few risks doing a disservice to the many others.

Nothing in this proposal implies disrespect to the current Queen or her predecessors, who have served our nation with grace and diligence. But part of our maturing as a young country is to better incorporate an ancient culture into our daily life. In many respects, the New Zealanders are more advanced than us in how they weave their traditional peoples into their social fabric. Unlike them, we do not have dual naming of our cities and institutions, a Powhiri welcome for official guests, or a spine-tingling Haka on the sporting field. So Australians should always be on the lookout for ways to deeply recognise our Indigenous heritage.

On the inexorable journey towards having one of our own as head of state, we have steadily cast off symbols of empire and replaced them with symbols that are more Australian: more small-'i' indigenous, if you like. Our current flag only became official when parliament passed the Flags Act in 1953. That was also the year when the first Australian appeared on a banknote. Our official anthem was 'God Save the Queen' until 1984. New citizens were required to pledge allegiance to the Queen until 1994.

Would anyone seriously now propose that we go back to pledging allegiance to the Queen in our citizenship ceremonies and singing God Save the Queen at national events? In the same vein, we should mark 2016 as the year when we put the first Australians on all our coins.

Reconciliation isn't just an economic and social challenge; it's a cultural one too. Egalitarians should support my proposal as a move towards greater racial equality. But the biggest supporters should be the traditionalists. After all, what could better acknowledge the past than recognising a history that goes back not just centuries, but tens of millennia?